Related papers: Enhancement of shock-capturing methods via machine…

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…

We present a novel deep learning method for estimating time-dependent parameters in Markov processes through discrete sampling. Departing from conventional machine learning, our approach reframes parameter approximation as an optimization…

We study experimental convergence rates of three shock-capturing schemes for hyperbolic systems of conservation laws: the second-order central-upwind (CU) scheme, the third-order Rusanov-Burstein-Mirin (RBM), and the fifth-order alternative…

Numerical simulation of ordinary differential equations (ODEs) can be challenging when the system exhibits high accelerations and rapidly changing dynamics. Under these conditions the ODE solver often needs to take very small time steps in…

We present a novel data-driven approach for enhancing gradient reconstruction in unstructured finite volume methods for hyperbolic conservation laws, specifically for the 2D Euler equations. Our approach extends previous structured-grid…

There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which…

Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…

Machine learning models play a vital role in the prediction task in several fields of study. In this work, we utilize the ability of machine learning algorithms to predict the occurrence of extreme events in a nonlinear mechanical system.…

Machine learned partial differential equation (PDE) solvers trade the reliability of standard numerical methods for potential gains in accuracy and/or speed. The only way for a solver to guarantee that it outputs the exact solution is to…

Solving partial differential equations (PDEs) has been a fundamental problem in computational science and of wide applications for both scientific and engineering research. Due to its universal approximation property, neural network is…

Deep learning methods for communications over unknown nonlinear channels have attracted considerable interest recently. In this paper, we consider semi-supervised learning methods, which are based on variational inference, for decoding…

Recurrent neural networks are machine learning algorithms which are suited well to predict time series. Echo state networks are one specific implementation of such neural networks that can describe the evolution of dynamical systems by…

The recently proposed high-order TENO scheme [Fu et al., Journal of Computational Physics, 305, pp.333-359] has shown great potential in predicting complex fluids owing to the novel weighting strategy, which ensures the high-order accuracy,…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

We propose Trusted Neural Network (TNN) models, which are deep neural network models that satisfy safety constraints critical to the application domain. We investigate different mechanisms for incorporating rule-based knowledge in the form…

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies,…

We develop data-driven methods for incorporating physical information for priors to learn parsimonious representations of nonlinear systems arising from parameterized PDEs and mechanics. Our approach is based on Variational Autoencoders…

This work studies an a posteriori data-driven approach (known as solver-in-the-loop) for sub-grid modeling of a shell model for turbulence. This approach takes advantage of the differentiable physics paradigm of deep learning, allowing a…

In this work we present an application of modern deep learning methodologies to the numerical solution of partial differential equations in transport models. More specifically, we employ a supervised deep neural network that takes into…

Deep neural network models have shown a great potential in accelerating the simulation of fluid dynamic systems. Once trained, these models can make inference within seconds, thus can be extremely efficient. However, they suffer from a…